Strong Convergence of an explicit iteration method in uniformly convex Banach spaces

Authors : Ahmed A ABDELHAKİM, R A RASHWAN

Pages : 178-187

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Publication Date : 2018-04-15

Article Type : Research Paper

Abstract :We obtain the necessary and sufficient conditions for the convergence of an explicit iterative procedure to a common fixed point of a finite family of non-self asymptotically quasi-nonexpansive type mappings in real Banach spaces. We also prove the strong convergence of this iterative method to a common fixed point of a finite family of non-self asymptotically quasi-nonexpansive in the intermediate sense mappings in uniformly convex Banach spaces. Our results mainly generalize and extend those obtained by Wang [L. Wang, Explicit iteration method for common fixed points of a finite family of nonself asymptotically nonexpansive mappings, Computers \& Mathematics with applications, 53, insert ignore into journalissuearticles values(2007);, 1012 - 1019.]
Keywords : common fixed point, iterative approximation, asymptotically quasi nonexpansive in the intermediate sense, uniformly convex Banach spaces